| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Topology and its Applications; v. 246, p. 9-21, SEP 1 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
We study the relations between a generalization of pseudocompactness, named (kappa, M)-pseudocompactness, the countably compactness of subspaces of beta omega and the pseudocompactness of their hyperspaces. We show, by assuming the existence of c-many selective ultrafilters, that there exists a subspace of beta omega that is (kappa, omega{*})-pseudocompact for all kappa < c, but CL(X) is not pseudocompact. We prove in ZFC that if omega subset of X subset of beta omega is such that X is (c, omega{*})-pseudocompact, then CL(X) is pseudocompact, and we further explore this relation by replacing c for some small cardinals. We provide an example of a subspace of beta omega for which all powers below eta are countably compact whose hyperspace is not pseudocompact, we show that if omega subset of X, the pseudocompactness of CL(X) implies that X is (kappa, omega{*})-pseudocompact for all kappa < eta, and provide an example of such an X that is not (b, omega{*})-pseudocompact. (C) 2018 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 16/26216-8 - Topology and sets |
| Grantee: | Artur Hideyuki Tomita |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 14/16955-2 - Outer measures by weak selections and hyperspaces. |
| Grantee: | Yasser Fermán Ortiz Castillo |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 17/15502-2 - Mad Families, Forcing and Combinatorial Principles in Topology |
| Grantee: | Vinicius de Oliveira Rodrigues |
| Support Opportunities: | Scholarships in Brazil - Doctorate |